An Elastoplastic Constitutive Model of Unsaturated Soils with Coupling of Capillary Hysteresis and Skeletal Deformation

Abstract

A constitutive model of unsaturated soils coupling skeletal deformation and capillary hysteresis is developed based on the modified Cam-clay model. To describe the effect of capillary hysteresis on skeletal deformation, an evolution equation is first developed for the degree of saturation to characterize the soil-water states under arbitrary drying/wetting conditions, and then a new hardening function is proposed, in which the matric suction and the degree of saturation as well as the plastic volumetric strain are simultaneously introduced to represent the hardening effect. It is shown that the proposed hardening function can properly capture the difference of preconsolidation pressure under different soil-water states and effectively describe the effect of drying/wetting history on the skeletal deformation. Theoretical simulations are compared to the experimental data available in the literature, showing that the new model captures very well the main features of unsaturated soil behavior. Unlike other unsaturated soil models, the new model treats the degree of saturation as an internal variable, whose evolution equation explicitly accounts for the capillary hysteresis. The new model can smoothly transit to the modified cam-clay model of saturated soils when the degree of saturation becomes one. The new constitutive model is implemented into a finite element code, U-DYSAC2, in which the displacement of solid skeleton, pore pressure and air pressure are primary nodal unknowns. An implicit algorithm is developed to integrate the constitutive relation at the Gaussian-point level. The proposed numerical procedure is used to simulate a typical two-dimensional unsaturated soil problem, illustrating the applicability and capabilities of the new numerical procedure.